The classical model of basal ganglia has been refined in recent years with discoveries of subpopulations within a nucleus and previously unknown projections. One such discovery is the presence of subpopulations of arkypallidal and prototypical neurons in external globus pallidus, which was previously considered to be a primarily homogeneous nucleus. Developing a computational model of these multiple interconnected nuclei is challenging, because the strengths of the connections are largely unknown. We therefore use a genetic algorithm to search for the unknown connectivity parameters in a firing rate model. We apply a binary cost function derived from empirical firing rate and phase relationship data for the physiological and Parkinsonian conditions. Our approach generates ensembles of over 1,000 configurations, or homologies, for each condition, with broad distributions for many of the parameter values and overlap between the two conditions. However, the resulting effective weights of connections from or to prototypical and arkypallidal neurons are consistent with the experimental data. We investigate the significance of the weight variability by manipulating the parameters individually and cumulatively, and conclude that the correlation observed between the parameters is necessary for generating the dynamics of the two conditions. We then investigate the response of the networks to a transient cortical stimulus, and demonstrate that networks classified as physiological effectively suppress activity in the internal globus pallidus, and are not susceptible to oscillations, whereas parkinsonian networks show the opposite tendency. Thus, we conclude that the rates and phase relationships observed in the globus pallidus are predictive of experimentally observed higher level dynamical features of the physiological and parkinsonian basal ganglia, and that the multiplicity of solutions generated by our method may well be indicative of a natural diversity in basal ganglia networks. We propose that our approach of generating and analyzing an ensemble of multiple solutions to an underdetermined network model provides greater confidence in its predictions than those derived from a unique solution, and that projecting such homologous networks on a lower dimensional space of sensibly chosen dynamical features gives a better chance than a purely structural analysis at understanding complex pathologies such as Parkinson's disease.

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour.

We simultaneously recorded local field potentials in the primary motor cortex and sensorimotor striatum in awake, freely behaving, 6-OHDA lesioned hemi-parkinsonian rats in order to study the features directly related to pathological states such as parkinsonian state and levodopa-induced dyskinesia. We analysed the spectral characteristics of the obtained signals and observed that during dyskinesia the most prominent feature was a relative power increase in the high gamma frequency range at around 80 Hz, while for the parkinsonian state it was in the beta frequency range. Here we show that during both pathological states effective connectivity in terms of Granger causality is bidirectional with an accent on the striatal influence on the cortex. In the case of dyskinesia, we also found a high increase in effective connectivity at 80 Hz. In order to further understand the 80- Hz phenomenon, we performed cross-frequency analysis and observed characteristic patterns in the case of dyskinesia but not in the case of the parkinsonian state or the healthy state. We noted a large decrease in the modulation of the amplitude at 80 Hz by the phase of low frequency oscillations (up to ~10 Hz) across both structures in the case of dyskinesia. This may suggest a lack of coupling between the low frequency activity of the recorded network and the group of neurons active at ~80 Hz.

The basal ganglia (BG) represent subcortical structures considered to be involved in action selection and decision making [1]. Dysfunction of the BG circuitry leads to many motor and cognitive disorders such as Parkinson’s disease (PD), Tourette syndrome, Huntington’s disease, obsessive compulsive disorder and many others. Therefore, we simultaneously recorded local field potentials (LFPs) in primary motor cortex and sensorimotor striatum to study features directly related to healthy versus pathological states such as Parkinson disease and levodopa-induced dyskinesia [2], [3]. The striatum, the input stage of the basal ganglia (BG), is an inhibitory network that contains several distinct cell types and receives massive excitatory inputs from the cortex. Cortex sends direct projections to the striatum, while striatum can affect cortex only indirectly through other BG nuclei and thalamus. Firstly we analyzed spectral characteristics of the obtained signals and observed that during dyskinesia, the most prominent feature was a relative power increase in the high gamma frequency range around 80 Hz, while for PD it was the beta frequency range. Secondly our preliminary results have shown that during both pathological states effective connectivity in terms of Granger causality is bidirectional with an accent on striatal influence on cortex. In the case of dyskinesia we have also found a specifically high increase in effective connectivity at 80 Hz. In order to further understand the 80-Hz phenomenon we have performed cross-frequency analysis across all states and both structures and observed characteristic patterns in the case of dyskinesia in both structures but not in the case of PD and healthy state. We have seen a large relative decrease in the modulation of the amplitude at 80Hz by the phase of low frequency oscillations (up to ~10Hz). It has been suggested that the activity of local neural populations is modulated according to the global neuronal dynamics in the way that populations oscillate and synchronize at lower frequencies and smaller ensembles are active at higher frequencies Our results suggest unexpectedly a lack of coupling between the low frequency activity of a larger population and the synchronized activity of a smaller group of neurons active at 80Hz.

Linkage between behavioral states and neural activity is one of the most important challenges in neuroscience. The network activity patterns in the awake resting state and in the actively behaving state in rodents are not well understood, and a better tool for differentiating these states can provide insights on healthy brain functions and its alteration with disease. Therefore, we simultaneously recorded local field potentials (LFPs) bilaterally in motor cortex and striatum, and measured locomotion from healthy, freely behaving rats. Here we analyze spectral characteristics of the obtained signals and present an algorithm for automatic discrimination of the awake resting and the behavioral states. We used the Support Vector Machine (SVM) classifier and utilized features obtained by applying discrete wavelet transform (DWT) on LFPs, which arose as a solution with high accuracy.

In the cortex, spontaneous neuronal avalanches can be characterized by spatiotemporal activity clusters with a cluster size distribution that follows a power law with exponent –1.5. Recordings in the striatum revealed that striatal activity was also characterized by spatiotemporal clusters that followed a power law distribution albeit, with significantly steeper slope, i.e., they lacked the large spatial clusters that are commonly expected for avalanche dynamics. In this study, we used computational modeling to investigate the influence of intrastriatal inhibition and corticostriatal interplay as important factors to understand the experimental findings and overall information transmission among these circuits.

Neuronal avalanches are found in the resting state activity of the mammaliancortex. Here we studied whether and how cortical avalanches are mappedonto the striatal circuitry, the first stage of the basal ganglia. We first demonstrate using organotypic cortex-striatum-substantia nigra cultures from rat that indeed striatal neurons respond to cortical avalanches originating in superficial layers. We simultaneously recorded spontaneous local field potentials (LFPs) in the cortical and striatal tissue using high-density microelectrode arrays. In the cortex, spontaneous neuronal avalanches were characterized by intermittent spatiotemporal activity clusters with a cluster size distribution that followed a power law with exponent 1.5. In the striatum, intermittent spatiotemporal activity was found to correlate with cortical avalanches. However, striatal negative LFP peaks (nLFPs) did not showavalanche signatures, but formed a cluster size distribution that had a much steeper drop-off, i.e., lacked large spatial clusters that are commonly expected for avalanche dynamics. The underlying de-correlation of striatal activity could have its origin in the striatum through local inhibition and/or could result from a particular mapping in the corticostriatal pathway. Here we show, using modeling, that highly convergent corticostriatal projections can map spatially extended cortical activity into spatially restricted striatal regimes.

Simultaneous oscillations in different frequency bands are implicated in the striatum, and understanding their interactions will bring us one step closer to restoring the spectral characteristics of striatal activity that correspond to the healthy state. We constructed a computational model of the striatum in order to investigate how different, simultaneously present, and externally induced oscillations propagate through striatal circuitry and which stimulation parameters have a significant contribution. Our results show that features of these oscillations and their interactions can be influenced via amplitude, input frequencies, and the phase offset between different external inputs. Our findings provide further untangling of the oscillatory activity that can be seen within the striatal network.

Network oscillations are ubiquitous across many brain regions. In the basal ganglia, oscillations are also present at many levels and a wide range of characteristic frequencies have been reported to occur during both health and disease. The striatum, the main input nucleus of the basal ganglia, receives massive glutamatergic inputs from the cortex and is highly susceptible to external oscillations. However, there is limited knowledge about the exact nature of this routing process and therefore, it is of key importance to understand how time-dependent, external stimuli propagate through the striatal circuitry. Using a network model of the striatum and corticostriatal projections, we try to elucidate the importance of specific GABAergic neurons and their interactions in shaping striatal oscillatory activity. Here, we propose that fast-spiking interneurons can perform an important role in transferring cortical oscillations to the striatum especially to those medium spiny neurons that are not directly driven by the cortical oscillations. We show how the activity levels of different populations, the strengths of different inhibitory synapses, degree of outgoing projections of striatal cells, ongoing activity and synchronicity of inputs can influence network activity. These results suggest that the propagation of oscillatory inputs into the medium spiny neuron population is most efficient, if conveyed via the fast-spiking interneurons. Therefore, pharmaceuticals that target fast-spiking interneurons may provide a novel treatment for regaining the spectral characteristics of striatal activity that correspond to the healthy state.

Several studies have shown a strong involvement of the basal ganglia (BG) in action selection and dopamine dependent learning. The dopaminergic signal to striatum, the input stage of the BG, has been commonly described as coding a reward prediction error (RPE), i.e. the difference between the predicted and actual reward. The RPE has been hypothesized to be critical in the modulation of the synaptic plasticity in cortico-striatal synapses in the direct and indirect pathway. We developed an abstract computational model of the BG, with a dual pathway structure functionally corresponding to the direct and indirect pathways, and compared its behaviour to biological data as well as other reinforcement learning models. The computations in our model are inspired by Bayesian inference, and the synaptic plasticity changes depend on a three factor Hebbian-Bayesian learning rule based on co-activation of pre- and post-synaptic units and on the value of the RPE. The model builds on a modified Actor-Critic architecture and implements the direct (Go) and the indirect (NoGo) pathway, as well as the reward prediction (RP) system, acting in a complementary fashion. We investigated the performance of the model system when different configurations of the Go, NoGo and RP system were utilized, e.g. using only the Go, NoGo, or RP system, or combinations of those. Learning performance was investigated in several types of learning paradigms, such as learning-relearning, successive learning, stochastic learning, reversal learning and a two-choice task. The RPE and the activity of the model during learning were similar to monkey electrophysiological and behavioural data. Our results, however, show that there is not a unique best way to configure this BG model to handle well all the learning paradigms tested. We thus suggest that an agent might dynamically configure its action selection mode, possibly depending on task characteristics and also on how much time is available.

The brain enables animals to behaviorally adapt in order to survive in a complex and dynamic environment, but how reward-oriented behaviors are achieved and computed by its underlying neural circuitry is an open question. To address this concern, we have developed a spiking model of the basal ganglia (BG) that learns to dis-inhibit the action leading to a reward despite ongoing changes in the reward schedule. The architecture of the network features the two pathways commonly described in BG, the direct (denoted D1) and the indirect (denoted D2) pathway, as well as a loop involving striatum and the dopaminergic system. The activity of these dopaminergic neurons conveys the reward prediction error (RPE), which determines the magnitude of synaptic plasticity within the different pathways. All plastic connections implement a versatile four-factor learning rule derived from Bayesian inference that depends upon pre- and post-synaptic activity, receptor type, and dopamine level. Synaptic weight updates occur in the D1 or D2 pathways depending on the sign of the RPE, and an efference copy informs upstream nuclei about the action selected. We demonstrate successful performance of the system in a multiple-choice learning task with a transiently changing reward schedule. We simulate lesioning of the various pathways and show that a condition without the D2 pathway fares worse than one without D1. Additionally, we simulate the degeneration observed in Parkinson's disease (PD) by decreasing the number of dopaminergic neurons during learning. The results suggest that the D1 pathway impairment in PD might have been overlooked. Furthermore, an analysis of the alterations in the synaptic weights shows that using the absolute reward value instead of the RPE leads to a larger change in D1.

The striatum, the input structure of the basal ganglia, is a major site learning and memory for goal-directed actions and habit formation. iny projection neurons of the striatum integrate cortical, thalamic, d nigral inputs to learn associations, with cortico-striatal synaptic asticity as a learning mechanism. Signaling molecules implicated in naptic plasticity are altered in alcohol withdrawal, which may ntribute to overly strong learning and increased alcohol seeking and nsumption. To understand how interactions among signaling molecules oduce synaptic plasticity, we implemented a mechanistic model of gnaling pathways activated by dopamine D1 receptors, acetylcholine ceptors, and glutamate. We use our novel, computationally efficient mulator, NeuroRD, to simulate stochastic interactions both within and tween dendritic spines. Dopamine release during theta burst and 20-Hz imulation was extrapolated from fast-scan cyclic voltammetry data llected in mouse striatal slices. Our results show that the combined tivity of several key plasticity molecules correctly predicts the currence of either LTP, LTD, or no plasticity for numerous perimental protocols. To investigate spatial interactions, we imulate two spines, either adjacent or separated on a 20-mu m ndritic segment. Our results show that molecules underlying LTP hibit spatial specificity, whereas 2-arachidonoylglycerol exhibits a atially diffuse elevation. We also implement changes in NMDA ceptors, adenylyl cyclase, and G protein signaling that have been asured following chronic alcohol treatment. Simulations under these nditions suggest that the molecular changes can predict changes in naptic plasticity, thereby accounting for some aspects of alcohol use sorder.

The nervous system encompasses structure and phenomena at different spatial and temporal scales from molecule to behavior. In addition, different scales are described by different physical and mathematical formalisms. The dynamics of second messenger pathways can be formulated as stochastic reaction-diffusion systems [1] while the electrical dynamics of the neuronal membrane is often described by compartment models and the Hodgkin-Huxley formalism. In neuroscience, there is an increasing need and interest to study multi-scale phenomena where multiple scales and physical formalisms are covered by a single model. While there exists simulators/frameworks, such as GENESIS and MOOSE [3], which span such scales (kinetikit/HH-models), most software applications are specialized for a given domain. Here, we report about initial steps towards a framework for multi-scale modeling which builds on the concept of multi-simulations [2]. We aim to provide a standard API and communication framework allowing parallel simulators targeted at different scales and/or different physics to communicate on-line in a cluster environment. Specifically, we show prototype work on simulating the effect on receptor induced cascades on membrane excitability. Electrical properties of a compartment model is simulated in MOOSE, while receptor induced cascades are simulated in NeuroRD [4,7] . In a prototype system, the two simulators are connected using PyMOOSE [5] and JPype [6]. The two models with their different physical properties (membrane currents in MOOSE, molecular biophysics in NeuroRD), are joined into a single model system. We demonstrate the interaction of the numerical solvers of two simulators (MOOSE, NeuroRD) targeted at different spatiotemporal scales and different physics while solving a multi-scale problem. We analyze some of the problems that may arise in multi-scale multi-simulations and present requirements for a generic API for parallel solvers. This work represents initial steps towards a flexible modular framework for simulation of large-scale multi-scale multi-physics problems in neuroscience. References 1. Blackwell KT: An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines. J Neurosci Meth 2006, 157: 142-153. 2. Djurfeldt M, Hjorth J, Eppler JM, Dudani N, Helias M, Potjans TC, Bhalla US, Diesmann M, Hellgren Kotaleski J, Ekeberg Ö: Run-Time Interoperability Between Neural Network Simulators Based on the MUSIC Framework. Neurinform 2010, 8: 43-60. 3. Dudani N, Ray S, George S, Bhalla US: Multiscale modeling and interoperability in MOOSE. Neuroscience 2009, 10(Suppl 1): 54. 4. Oliveira RF, Terrin A, Di Benedetto G, Cannon RC, Koh W, Kim M, Zaccolo M, Blacwell KT: The Role of Type 4 Phosphdiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations.

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

1. The glutamatergic synapses formed between the unbranched giant reticulospinal axons onto spinal neurons in lamprey offer a central vertebrate synapse in which the presynaptic element can be impaled with one or several microelectrodes, which may be used for recording as well as microinjection of different substances. To provide a basis for the use of this synapse in studies of release mechanisms, we have examined the use-dependent modulation of the synaptic response under conditions of conventional cell body stimulation, and during direct stimulation of the presynaptic axon. 2. To examine the stability of the mixed electrotonic and chemical reticulospinal excitatory postsynaptic potential (EPSP) over time, action potentials were evoked at a rate of 1 Hz for 800-1000 trials. In three out of seven synapses the chemical component remained at a similar amplitude, while in four cases a progressive decrease (up to 35%) occurred. The electrotonic component remained at a similar amplitude in all cases. 3. During paired pulse stimulation of the reticulospinal cell body (pulse interval 65 ms) the chemical EPSP component showed a net facilitation in all cases tested [from 0.64 +/- 0.35 to 0.89 +/- 0.48 (SD) mV, n = 13], while the peak amplitude of the electrotonic component was unchanged (1.37 +/- 0.68 and 1.36 +/- 0.66 mV, respectively). Recording of the axonal action potential during paired pulse stimulation showed that the width of the first and second action potential did not differ [1/2 width (2.48 +/- 0.39 ms and 2.48 +/- 0.42 ms, respectively; n = 8)]. 4. The degree of facilitation varied markedly between different synapses, ranging from an increase of a few percent to a two-fold increase (24 +/- 16% mean change of total EPSP amplitude, corresponding to 44 +/- 26% mean change of chemical EPSP amplitude). This type of variability was also observed in synapses made from the same unbranched reticulospinal axon onto different postsynaptic cells. 5. When paired pulse stimulation was applied to the reticulospinal axon in the very vicinity of the synaptic area (0.1-1 mm) a net depression of the chemical component occurred in 11 out of 19 cases, and in the remaining cases the level of net facilitation was lower as compared with cell body stimulation (range between +17 and -23% change of total EPSP amplitude; mean -5%; n = 19). 6. To test if the change of the EPSP plasticity during local stimulation correlated with an increased transmitter release, two microelectrodes were placed in the same reticulospinal axon at different distances from the synaptic area.(ABSTRACT TRUNCATED AT 400 WORDS)

Realistic bottom-up modelling has been seminal to understanding which properties of microcircuits control their dynamic behaviour, such as the locomotor rhythms generated by central pattern generators. In this article of the TINS Microcircuits Special Feature, we review recent modelling work on the leech-heartbeat and lamprey-swimming pattern generators as examples. Top-down mathematical modelling also has an important role in analyzing microcircuit properties but it has not always been easy to reconcile results from the two modelling approaches. Most realistic microcircuit models are relatively simple and need to be made more detailed to represent complex processes more accurately. We review methods to add neuromechanical feedback, biochemical pathways or full dendritic morphologies to microcircuit models. Finally, we consider the advantages and challenges of full-scale simulation of networks of microcircuits.

MUSIC is an API allowing large scale neuron simulators using MPI internally to exchange data during runtime. We provide experiences from the adaptation of two neuronal network simulators of diﬀerent kinds, NEST and MOOSE, to this API. A multi-simulation of a cortico-striatal network model involving both simulators is performed, demonstrating how MUSIC can promote inter-operability between models written for diﬀerent simulators and how these can be re-used to build a larger model system. We conclude that MUSIC fulﬁlls the design goals of being portable and simple to adapt to existing simulators. In addition, since the MUSIC API enforces independence between the applications, the multi-simulationcould be built from pluggable component modules without adaptation of the components to each other in terms of simulation time-step or topology of connections between the modules.

Striatal spiny projection neurons (SPNs) receive convergent excitatory synaptic inputs from the cortex and thalamus. Activation of spatially clustered and temporally synchronized excitatory inputs at the distal dendrites could trigger plateau potentials in SPNs. Such supralinear synaptic integration is crucial for dendritic computation. However, how plateau potentials interact with subsequent excitatory and inhibitory synaptic inputs remains unknown. By combining computational simulation, two-photon imaging, optogenetics, and dual-color uncaging of glutamate and GABA, we demonstrate that plateau potentials can broaden the spatiotemporal window for integrating excitatory inputs and promote spiking. The temporal window of spiking can be delicately controlled by GABAergic inhibition in a cell-type–specific manner. This subtle inhibitory control of plateau potential depends on the location and kinetics of the GABAergic inputs and is achieved by the balance between relief and reestablishment of NMDA receptor Mg2+ block. These findings represent a mechanism for controlling spatiotemporal synaptic integration in SPNs.

The scientific mission of the Computational Brain Science Lab at CSC is to be at the forefront of mathematical modelling, quantitative analysis and mechanistic understanding of brain function. We perform research on (i) computational modelling of biological brain function and on (ii) developing theory, algorithms and software for building computer systems that can perform brain-like functions. Our research answers scientific questions and develops methods in these fields. We integrate results from our science-driven brain research into our work on brain-like algorithms and likewise use theoretical results about artificial brain-like functions as hypotheses for biological brain research.

Our research on biological brain function includes sensory perception (vision, hearing, olfaction, pain), cognition (action selection, memory, learning) and motor control at different levels of biological detail (molecular, cellular, network) and mathematical/functional description. Methods development for investigating biological brain function and its dynamics as well as dysfunction comprises biomechanical simulation engines for locomotion and voice, machine learning methods for analysing functional brain images, craniofacial morphology and neuronal multi-scale simulations. Projects are conducted in close collaborations with Karolinska Institutet and Karolinska Hospital in Sweden as well as other laboratories in Europe, U.S., Japan and India.

Our research on brain-like computing concerns methods development for perceptual systems that extract information from sensory signals (images, video and audio), analysis of functional brain images and EEG data, learning for autonomous agents as well as development of computational architectures (both software and hardware) for neural information processing. Our brain-inspired approach to computing also applies more generically to other computer science problems such as pattern recognition, data analysis and intelligent systems. Recent industrial collaborations include analysis of patient brain data with MentisCura and the startup company 13 Lab bought by Facebook.

Our long term vision is to contribute to (i) deeper understanding of the computational mechanisms underlying biological brain function and (ii) better theories, methods and algorithms for perceptual and intelligent systems that perform artificial brain-like functions by (iii) performing interdisciplinary and cross-fertilizing research on both biological and artificial brain-like functions.

On one hand, biological brains provide existence proofs for guiding our research on artificial perceptual and intelligent systems. On the other hand, applying Richard Feynman’s famous statement ”What I cannot create I do not understand” to brain science implies that we can only claim to fully understand the computational mechanisms underlying biological brain function if we can build and implement corresponding computational mechanisms on a computerized system that performs similar brain-like functions.

The basal ganglia are a group of subcortical nuclei that play a prominent role in motor function in mammals as well as in lamprey. The aim of the present study was to characterize the different components of the lamprey basal ganglia, and determine to what extent they correspond to those found in the mammalian basal ganglia. Anatomical tract tracing, immunohistochemistry and acute brain slice patch clamp recordings were employed to address this question.Two pallidal regions were identified in the lamprey; one region, considered homologous to the mammalian globus pallidus, was located ventral to the ementia thalami on the telencephalic/diencephalic border. It receives striatal input from inwardly rectifying neurons (IRNs) and contains GABAergic projection neurons, of which those projecting to the tectum were shown to be tonically active. It also contains neurons immunoreactive for parvalbumin. Separate subpopulations of pallidal neurons project to the optic tectum, the diencephalic and mesencephalic locomotor regions (MLR).Another region, in the midbrain, considered homologous to the substantia nigra pars reticulata receives input from a different subset of IRNs and sends GABAergic projections to the tectum and the diencephalic locomotor region. This midbrain region also contains parvalbumin immunoreactive neurons. The main population of striatal neurons, IRNs, displays the anatomical and electrophysiological hallmarks of mammalian medium spiny neurons, including inward rectification and ramping responses to first spike. It also contains neurons with properties similar to fast-spiking neurons. The striatum receives pallial and thalamic input as well as ascending dopaminergic, serotonergic and histaminergic inputs, similar to that in mammals.Our results suggest that the basic features of the basal ganglia with regard to both structure and function are conserved throughout the vertebrate phylogeny, including striatal/pallidal subdivisions.

Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours. Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building.

If we are to understand how the brain performs different integrated functions in cellular terms, we need both to understand all relevant levels of analysis from the molecular to the behavioural and cognitive levels and to realize an integration of such levels. This is currently a major challenge for neuroscience. Most research, whether dealing with perception, action or learning, focuses on a few levels of organization, for instance the molecular level and brain imaging, and leaves other crucial areas practically untouched. To reach the level of understanding that we desire, a multi-level approach is required in which the different levels link into each other. It is possible to bridge across the different levels for one system, and this has been demonstrated, for example, in the lamprey in generation of goal-directed locomotion. It can be argued that an integrated analysis of any neural system cannot be performed without the aid of a close interaction between experiments and modelling. The dynamic processing within any neural system is such that an intuitive interpretation is rarely sufficient.

The nervous system contains a toolbox of motor programs in the brainstem and spinal cord--that is, neuronal networks designed to handle the basic motor repertoire required for survival, including locomotion, posture, eye movements, breathing, chewing, swallowing and expression of emotions. The neural mechanisms responsible for selecting which motor program should be recruited at a given instant are the focus of this review. Motor programs are kept under tonic inhibition by GABAergic pallidal neurons (the output nuclei of the basal ganglia). The motor programs can be relieved from pallidal inhibition through activation of striatal neurons at the input stage of the basal ganglia. It is argued that the striatum has a prominent role in selecting which motor program should be called into action.

The lamprey is one of the few vertebrates in which the neural control system for goal-directed locomotion including steering and control of body orientation is well described at a cellular level. In this report we review the modeling of the central pattern-generating network, which has been carried out based on detailed experimentation. In the same way the modeling of the control system for steering and control of body orientation is reviewed, including neuromechanical simulations and robotic devices.

The convergence of corticostriatal glutamate and dopamine from the midbrain in the striatal medium spiny neurons (MSN) triggers synaptic plasticity that underlies reinforcement learning and pathological conditions such as psychostimulant addiction. The increase in striatal dopamine produced by the acute administration of psychostimulants has been found to activate not only effectors of the AC5/cAMP/PKA signaling cascade such as GluR1, but also effectors of the NMDAR/Ca2+/RAS cascade such as ERK. The dopamine-triggered effects on both these cascades are mediated by D1R coupled to Golf but while the phosphorylation of GluR1 is affected by reductions in the available amount of Golf but not of D1R, the activation of ERK follows the opposite pattern. This segregation is puzzling considering that D1R-induced Golf activation monotonically increases with DA and that there is crosstalk from the AC5/cAMP/PKA cascade to the NMDAR/Ca2+/RAS cascade via a STEP (a tyrosine phosphatase). In this work, we developed a signaling model which accounts for this segregation based on the assumption that a common pool of D1R and Golf is distributed in two D1R/Golf signaling compartments. This model integrates a relatively large amount of experimental data for neurons in vivo and in vitro. We used it to explore the crosstalk topologies under which the sensitivities of the AC5/cAMP/PKA signaling cascade to reductions in D1R or Golf are transferred or not to the activation of ERK. We found that the sequestration of STEP by its substrate ERK together with the insensitivity of STEP activity on targets upstream of ERK (i.e. Fyn and NR2B) to PKA phosphorylation are able to explain the experimentally observed segregation. This model provides a quantitative framework for simulation based experiments to study signaling required for long term potentiation in MSNs.

Slow Ca2(+) oscillations caused by release from intracellular stores have been observed in neurons in the lamprey spinal cord. These oscillations are triggered by activation of metabotropic glutamate receptors on the cell surface. The pathway leading from receptor activation to the inositol triphosphate-mediated release of Ca2(+) from the endoplasmatic reticulum has been modelled in order to facilitate further understanding of the nature of these oscillations. The model generates Ca2(+) oscillations with a frequency range of 0.01-0.09 Hz. A prediction of the model is that the frequency will increase with a stronger extracellular glutamate signal.

Slow Ca2+ oscillations caused by release from intracellular stores have been observed in neurons in the lamprey spinal cord. These oscillations are triggered by activation of metabotropic glutamate receptors on the cell surface. The pathway leading from receptor activation to the inositol triphosphate-mediated release of Ca2+ from the endoplasmatic reticulum has been modelled in order to facilitate further understanding of the nature of these oscillations. The model generates Ca2+ oscillations with a frequency range of 0.01-0.09 Hz. A prediction of the model is that the frequency will increase with a stronger extracellular glutamate signal.

A biochemical model is developed for the receptor, G-protein and effector (RGE) steps of olfactory signal transduction in the cilia of the vertebrate olfactory receptor neurons (ORNs). It describes the steps from odorant binding to activation of the effector enzyme, which catalyzes the conversion of ATP to cAMP. In the cilia of the olfactory receptor neurons (ORNs), cAMP regulates cyclic nucleotide gated channels, which in turn control Ca influx and Ca dependent activation of chloride conductances. As a result the cilia potential becomes depolarized.

A biochemical model of the receptor, G-protein and effector (RGE) interactions during transduction in the cilia of vertebrate olfactory receptor neurons (ORNs) was developed and calibrated to experimental recordings of cAMP levels and the receptor current (RC). The model describes the steps from odorant binding to activation of the effector enzyme which catalyzes the conversion of ATP to cAMP, and shows how odorant stimulation is amplified and delayed by the RGE transduction cascade. A time-dependent sensitivity analysis was performed on the model. The model output-the cAMP production rate-is particularly sensitive to a few, dominant parameters. During odorant stimulation it depends mainly on the initial density of G-proteins and the catalytic constant for cAMP production.

Mechanisms underlying lotal bursting as well as coordinationbetween different levels of a spinal CPG generating locomotionhave been investigated using computer simulations. A"primitive" jawless vertebrate, the lamprey, is used a.s aprototype model. Most simulations have been conducted using abiophysical neu ron model built on the Hodgkin-Huxley formalismand equipped with Nu+, K+,Ca²+, Kca, LVACa²+ and NMDA activated channels. Inhibitory andexcitatory AMPA/kainate and NMDA synapses are modeled as timedependent conductances with appropriate reversal potentials.For tomparison, Morris-Letar oscillators as well as adaptingleaky integrator-like units are also used.

The basic identified building blocks of the CPG, generatingalternating left right burst activity, tonsist of ipsilaterallyprojecting excitatory neurons (E) and contralaterallyprojecting inhibitory neurons (C). The model neurons are connected in the same way ss has been established experimentally.Sinte several complementary mechanisms may play a role, thepotential of two different neural mechanisms have been exploredwhich can provide burst activity at the segmen tal level, andintersegmental coordination. When alternating left-rightactivity is produced through an escape-like mechanism the quietside is able to become ac tive despite ongoing inhibition fromthe contralateral side. Reciprocal inhibition is then a crucialburst terminating factor. Burst frequency is strongly affectedby the effective inhibition and the drive to escape fromongoing inhibition. Several factors influence this process. Kcacurrents control spike frequency on the active sideand also a post-burst hyperpolarization on the inactive side.Postin hibitory rebound properties, carried by e.g. low voltageactivatedCa²+ currents further can promote escape. Phasicipsilateral excitation and NMDA membrane properties stabilizethe rhythm, especially in the lower frequency range. Severalexperimental observations can be explained based on the effectthese different factors have on effective inhibition andtendency for escape.

Bursting can, however, also be produced by a networkdeprived of inhibition, showing that powerful burst terminatingmechanisms not requiring inhibition exist. In the model withbiophysically detailed neurons such a mechanism could beactivation ofKcacurrents due to accumulation ofCa²+ during the active phase. As shown innon-spiking, as well as biophysically detailed models, aconstant burst proportion over a wide frequency range can beachieved by modulation of the rel ative strength of adaptationin such networks. The left-right inhibition causes left-rightalternation but may not affect the frequency of bursting.

When both types of lotal oscillatory networks are extendedlongitudinally, a rostral to caudal phase delay is producedwhen caudal projections are extended further than the rostralenes. However, the excitatory versus inhibitory projec tionsmay have different roles in the two alternative models. Thisrelative phase delay expressed as % of cycle duration,increases in general with frequency. The simulations suggestthat the conditions at the ends of the simulated chain arecritical for the resulting phase lag. The capability ofbuffering against frequency variations and rapid adjustmentsfollowing perturbations is discussed and com pared with chainsof relaxation oscillators and phase-coupled oscillators.

Pairing specific LTD (PSD) is produced by paired parallel fiber (PF) and climbing fiber (CF) stimulation and requires Ca2+ elevation. CF or PF activation cause Ca2+ increase through voltage dependent channels and IP3 induced Ca2+ release, respectively. We developed a model of Ca2+ dynamics in Purkinje cell spines to investigate why paired PF-CF activation is necessary for PSD. Simulations show a supralinear increase of the Ca2+ signal if the CF input occurs in a restricted time interval following the PF input. Ca2- buffers significantly contribute to this phenomenon. This mechanism may be involved in the requirement of temporal specificity in classical conditioning.

Realistic computer simulations of the experimentally established local spinal cord neural network generating swimming in the lamprey have been performed. Populations of network interneurons were used in which cellular properties, like cell size and membrane conductance including voltage dependent ion channels were randomly distributed around experimentally obtained mean values, as were synaptic conductances (kainate/AMPA, NMDA, glycine) and delays. This population model displayed more robust burst activity over a wider frequency range than the more simple subsample model used previously, and the pattern of interneuronal activity was appropriate. The strength of the reciprocal inhibition played a very important role in the regulation of burst frequency, and just by changing the inhibitory bias the entire physiological range could be covered. At the lower frequency range of bursting the segmental excitatory interneurons provide stability as does the activation of voltage dependent NMDA receptors. Spike frequency adaptation by means of summation of afterhyperpolarization (AHP) serves as a major burst terminating factor, and at lower rates the membrane properties conferred by the NMDA receptor activation. The lateral interneurons were not of critical importance for the burst termination. They may, however, be of particular importance for inducing a rapid burst termination during for instance steering and righting reactions. Several cellular factors combine to provide a secure and stable motor pattern in the entire frequency range.

Factors contributing to the production of a phase lag along chains of oscillatory networks consisting of Hodgkin-Huxley type neurons are analyzed by means of simulations. Simplified network configurations are explored consisting of the basic building blocks of the spinal central pattern generator (CPG) generating swimming in the lamprey. It consists of reciprocally coupled crossed inhibitory C interneurons and ipsilateral excitatory E interneurons that activate C neurons and other E neurons. Oscillatory activity in the model network can, in the simplest case, be produced by a pair of reciprocally coupled C interneurons oscillating through an escape mechanism. Different levels of tonic excitation drive the network over a wide burst frequency range. In this type of network, powerful frequency-regulating factors are the effective inhibition produced by the active side, in combination with the tendency of the inactive side to escape from the inhibition. These two mechanisms can be affected by several factors, e.g. spike frequency adaptation (calcium-dependent K+ channels): N-methyl-D-aspartate membrane properties as well as presence of low-voltage activated calcium channels. A rostrocaudal phase lag can be produced either by extending the contralateral inhibitory projections or the ipsilateral excitatory projections relatively more in the caudal than the rostral direction, since both an increased inhibition and a phasic excitation slow down the receiving network. The phase lag becomes decreased if the length of the intersegmental projections is increased or if the projections are extended symmetrically in both the rostral and the caudal directions. The simulations indicate that the conditions in the ends of an oscillator chain may significantly affect sign, magnitude and constancy of the phase lag. Also, with short and relatively weak intersegmental connections, the network remains robust against perturbations as well as intrinsic frequency differences along the chain. The phase lag (percentage of cycle duration) increases, however, with burst frequency also when the coupling strength is comparatively weak. The results are discussed and compared with previous "phase pulling" models as well as relaxation oscillators.

In adult cats the whole S1 and rostral half of the L7 dorsal roots were cut on the left side of the spinal cord to produce a partial monosynaptic deafferentation of the ipsilateral alpha-motoneurons. Three, 6 or 12 weeks later, monosynaptic reflexes (MSRs) were recorded from the L6, L7 and S1 ventral roots or from various peripheral nerves during stimulation of the L6 and remaining parts of the L7 dorsal roots. Also, monosynaptic excitatory postsynaptic potentials (EPSPs) were recorded intracellularly in different types of medial gastrocnemius alpha-motoneurons of the L7 segment during stimulation of various hind limb muscle nerves. The right side with an identical acute deafferentation served as control. On the chronically lesioned side the MSRs were increased in size, also during post-tetanic potentiation. The monosynaptic EPSPs had increased amplitudes in all motoneuron types, but the relation in EPSP size between different motoneuron types as well as between different synergistic inputs remained largely unchanged. EPSP rise times were not changed, and aberrant monosynaptic connections from non-synergist muscles were not observed. It is concluded that the extent of reactive reflex changes may be related to both the number of vacant synaptic sites and the degree of functional synergism between the eliminated and remaining monosynaptic pathways. Possible underlying mechanisms are discussed.

Metabotropic glutamate receptor (mGluR) activation modulates the lamprey spinal locomotor network. Potentiation of the NMDA receptor current is observed suggesting that one possible mechanism for mGluR to regulate locomotion is through such an interaction. The present study investigates this possibility. The behavior of NMDA induced oscillations are explored when potentiation is achieved of different contributing factors of the NMDA receptor current. The effects on the duration of the depolarized phase as well as hyperpolarized interval depend on both level of activation and holding potential of the cells. From these effects on the cell level the network effects are predicted.

Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-D-aspartate (NMDA) and x-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations. The bursting mechanism relies on intracellular accumulation of calcium that activates Ca2+-dependent KC The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry following the action potential, Ca-AP pool, and the other represents the calcium inflow through the NMDA channels, Ca-NMDA pool. The Ca2+-dependent K+ activated by these two calcium pools are referred to as K-CaAP and K-CaNMDA respectively, and their relative conductances are modulated and increase with the background activation of the network. When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of 0.5-5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA. When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal strength, this kind of network is capable of reproducing several experimental observations such as those occurring during strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst intervals at different levels of the spinal cord.

Classical conditioning of the nictitating membrane response requires a specific temporal interval between conditioned stimulus and unconditioned stimulus, and produces an increase in Protein Kinase C (PKC) activation in Purkinje cells. To evaluate whether biochemical interactions within the Purkinje cell may explain the temporal sensitivity, a model of PKC activation by Ca2+, diacylglycerol (DAG), and arachidonic acid (AA) is developed. Ca2+ elevation is due to CF stimulation and IP3 induced Ca2+ release (IICR). DAG and IP3 result from PF stimulation, while AA results from phospholipase A2 (PLA(2)). Simulations predict increased PKC activation when PF stimulation precedes CF stimulation by 0.1 to 3 s. The sensitivity of IICR to the temporal relation between PF and CF stimulation, together with the buffering system of Purkinje cells, significantly contribute to the temporal sensitivity.

Striatal fast spiking (FS) interneurons provide inhibition to each other as well as to medium spiny projection (SP) neurons. They exhibit up-states synchronously with SP neurons, and receive GABAergic and AMPA synaptic input during both up- and down-states. The synaptic input during down-states can be considered noise and might affect detection of up-states. We investigate what role this background noise might play for up-state firing in a 127 compartment FS model neuron. The model has Na, KDr and KA conductances, and is activated through AMPA and GABA synapses. The model's response to current injection and synaptic inputs resembled experimental data. We show that intermediate levels of noise neither facilitates nor degrades the ability of the FS neuron model to detect up-states.

Using potassium currents to solve signal-to-noise problems in inhibitory feedforward networks of the striatum. J Neurophysiol 95: 331 - 341, 2006. First published September 28, 2005; doi: 10.1152/jn. 00063.2005. Fast-spiking (FS) interneurons provide the main route of feedforward inhibition from cortex to spiny projection neurons in the striatum. A steep current-firing frequency curve and a dense local axonal arbor suggest that even small excitatory inputs could translate into powerful feedforward inhibition, although such an arrangement is also sensitive to amplification of spurious synaptic inputs. We show that a transient potassium (KA) current allows the FS interneuron to strike a balance between sensitivity to correlated input and robustness to noise, thereby increasing its signal-to-noise ratio (SNR). First, a compartmental FS neuron model was created to match experimental data from striatal FS interneurons in cortex - striatum - substantia nigra organotypic cultures. Densities of sodium, delayed rectifier, and KA channels were optimized to replicate responses to somatic current injection. Spontaneous alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and gamma-aminobutyric acid ( GABA) synaptic currents were adjusted to the experimentally measured amplitude, rise time, and interevent interval histograms. Second, two additional adjustments were required to emulate the remaining experimental observations. GABA channels were localized closer to the soma than AMPA channels to match the synaptic population reversal potential. Correlation among inputs was required to produce the observed firing rate during up-states. In this final model, KA channels were essential for suppressing down-state spikes while allowing reliable spike generation during up-states. This mechanism was particularly important under conditions of high dopamine. Our results suggest that KA channels allow FS interneurons to operate without a decrease in SNR during conditions of increased dopamine, as occurs in response to reward or anticipated reward.

Factors controlling burst proportion in oscillatory networks are analyzed. This question is motivated by the lamprey swimming motor pattern which, independently on burst frequency, is characterized by a constant burst proportion. We investigate the effect of active modulation of the relative influence of a slower and faster adaptation controlling the depolarized phase. Using Morris–Lecar oscillators, NMDA-dependent oscillations or a network of mutually excitatory neurons, it is shown that the burst proportion can be controlled by increasing what corresponds to adaptation. Oscillations occur over an extended range of background stimulation values, leading to a higher maximal frequency.